Analysis and Control of HIV Dynamic Models

Abstract

Lakshmi N Sridhar

HIV/AIDS has significantly impacted universities, affecting young students through increased illness, mortality, and absenteeism, as well as impacting institutional functioning and resources. Universities, particularly in regions with high HIV prevalence, have had to develop strategies to address the epidemic, including prevention, care, and support programs, as well as integrating HIV/AIDS education into the curriculum. In this work, bifurcation analysis and multiobjective nonlinear model predictive control is performed on three HIV dynamic models, Bifurcation analysis is a powerful mathematical tool used to deal with the nonlinear dynamics of any process. Several factors must be considered, and multiple objectives must be met simultaneously. Bifurcation analysis and multiobjective nonlinear model predictive control (MNLMPC) calculations are performed on three oncolytic dynamic models. The MATLAB program MATCONT was used to perform the bifurcation analysis. The MNLMPC calculations were performed using the optimization language PYOMO in conjunction with the state-of-the-art global optimization solvers IPOPT and BARON. The bifurcation analysis revealed the existence of branch and limit points in the models. The branch and limit points (which cause multiple steady-state solutions from a singular point) are very beneficial because they enable the Multiobjective nonlinear model predictive control calculations to converge to the Utopia point ( the best possible solution) in all the models.

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